Math 7 · Unit 13: Probability · Cambridge Lower Secondary Maths Stage 7

Questions

1. 1. Question 1a: a gardener plants 45 seeds and 31 of the seeds grow successfully. Work out the experimental probability that a seed will grow successfully.

   • 45/31
   • 31/45
   • 14/45
   • 31/76
   Check

2. 2. Question 1b: 31 of 45 seeds grow. Work out the experimental probability that a seed will not grow successfully.

   • 14/31
   • 1/45
   • 31/45
   • 14/45
   Check

3. 3. Question 2a: 378 babies are weighed. 125 have a mass of less than 3 kg. Work out the experimental probability that a baby has a mass of less than 3 kg.

   • 3/378
   • 253/378
   • 125/378
   • 125/253
   Check

4. 4. Question 2b: 125 of 378 babies have a mass of less than 3 kg. What is the experimental probability that a baby has a mass of at least 3 kg?

   • 253/125
   • 1/3
   • 125/378
   • 253/378
   Check

5. 5. Question 3a: A call centre receives 200 calls. The table shows how long a caller must wait before speaking to a customer service officer. Work out the experimental probability that a caller will wait less than 2 minutes.

   • 43/157
   • 64/200
   • 43/200
   • 21/200
   Check

6. 6. Question 3b: A call centre receives 200 calls. The table shows how long a caller must wait. Work out the experimental probability that a caller will wait between 2 and 3 minutes.

   • 110/200
   • 153/200
   • 67/200
   • 43/200
   Check

7. 7. Question 3c: A call centre receives 200 calls. The table shows how long a caller must wait. Work out the experimental probability that a caller will wait at least 3 minutes.

   • 148/200
   • 11/20
   • 9/20
   • 37/100
   Check

8. 8. Question 4a: The heights of 234 young men, aged 20 to 29 years, are measured. Work out the experimental probability that the height of a man is less than 165 cm.

   • 28/100
   • 28/206
   • 160/234
   • 14/117
   Check

9. 9. Question 4b: The heights of 234 young men are measured. Work out the experimental probability that the height of a man is 180 cm or less.

   • 94/117
   • 160/234
   • 46/234
   • 188/206
   Check

10. 10. Question 4c: The heights of 234 young men are measured. Work out the experimental probability that the height of a man is 165 cm or more.

    • 28/234
    • 46/234
    • 103/117
    • 160/234
    Check

11. 11. Question 5a: The lights of 20 cars are tested. The car could pass (P) or fail (F). Here are the results: PPPPP PPPPF PFPPPP PPPP. Work out the experimental probability that a car will pass, and that a car will fail.

    • Pass 1/10, fail 9/10
    • Pass 9/10, fail 1/10
    • Pass 4/5, fail 1/5
    • Pass 9/10, fail 1/9
    Check

12. 12. Question 5b: The first 20 cars were PPPPP PPPPF PFPPPP PPPP. The results for another 20 cars are PPFPP FPPPP PPPPF FPPPP. Recalculate the probabilities that a car will pass and that a car will fail, based on all 40 cars.

    • Pass 3/20, fail 17/20
    • Pass 17/20, fail 3/20
    • Pass 9/10, fail 1/10
    • Pass 4/5, fail 1/5
    Check

13. 13. Question 5c: why are the second experimental probabilities (based on 40 cars) more reliable than the first (based on 20 cars)?

    • They are based on more trials (40 cars instead of 20).
    • They are based on fewer cars.
    • The probability is higher.
    • The second cars were newer.
    Check

14. 14. Question 6a: A woman travels to work on a bus each morning. She keeps a record for 30 days. The bus is late nine times. Work out the experimental probability that the bus will be late, and that it will be on time.

    • Late 7/10, on time 3/10
    • Late 9/21, on time 21/30
    • Late 1/9, on time 8/9
    • Late 3/10, on time 7/10
    Check

15. 15. Question 6b: In the next 25 days the bus is late four times. Use all the results (late 9 times in 30 days, then 4 times in 25 days) to find the experimental probability that the bus will be late, and that it will be on time.

    • Late 42/55, on time 13/55
    • Late 3/10, on time 7/10
    • Late 13/55, on time 42/55
    • Late 4/25, on time 21/25
    Check

16. 16. Question 6c: the bus was late 13 times in 55 days. The woman predicts it will be late 24 times in the next 100 days. How did she work this out?

    • She used 9 + 4 + 11 = 24.
    • 13/55 is about 0.24, and 0.24 × 100 = 24.
    • She used 24 = 100 − 76.
    • She used the first 30 days only: 9/30 × 100.
    Check

17. 17. Question 7a: A computer simulates spinning three coins 160 times and records the number of heads. Work out the experimental probability of getting three heads, three tails, and at least two heads.

    • Three heads 7/80, three tails 17/160, at least two heads 41/80
    • Three heads 17/160, three tails 7/80, at least two heads 41/80
    • Three heads 7/80, three tails 61/160, at least two heads 41/80
    • Three heads 7/80, three tails 17/160, at least two heads 17/80
    Check

18. 18. Question 7b: A teacher says the theoretical probability of getting three heads is 1/8 = 20/160. How does it compare with the experimental probability of getting three heads?

    • The experimental probability is more.
    • They are equal.
    • The experimental probability is a little less.
    • They cannot be compared.
    Check

19. 19. Question 7c: What can you say about the theoretical and experimental probabilities for getting zero heads?

    • The experimental probability is much more.
    • They are equal.
    • The theoretical probability is 0.
    • They are close (0.125 and about 0.106).
    Check

20. 20. Question 8a: A computer simulates throwing two dice and adding the scores together, 100 times. Work out the experimental probability of getting a score of 7, more than 7, less than 7, and 12.

    • 7 is 17/100, more than 7 is 47/100, less than 7 is 9/25, 12 is 1/50
    • 7 is 17/100, more than 7 is 36/47, less than 7 is 47/100, 12 is 2/17
    • 7 is 17/100, more than 7 is 9/25, less than 7 is 47/100, 12 is 1/50
    • 7 is 1/6, more than 7 is 9/25, less than 7 is 47/100, 12 is 1/36
    Check